files / problems / hilbert16-limit-cycles / compute / q3 / kk-plus-one / certs / core.json

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{
  "Pt00": "-15/2",
  "Qt00": "-2",
  "a": "2",
  "b": "-15/2",
  "circle_line_disc": "-54000",
  "claim": "Translate the radial cubic at p=(2,0), multiply by the line 4x-15y, and prove that line misses the translated circle. The translated circle remains a periodic orbit of the degree-4 product. Not two hyperbolic cycles and not a bound on H(n).",
  "cycles_proved": 1,
  "degree": 4,
  "hn_moved": false,
  "hopf_cycles_written": false,
  "imagined_two_cycles": false,
  "jac_det": "0",
  "jac_trace": "0",
  "line": "4x-15y",
  "line_misses_circle": true,
  "miss_cleared": "4*8^2-241=15",
  "miss_inequality": "8/sqrt(241) > 1/2",
  "n_plus_2_degree": 5,
  "rho2": "1/4",
  "schema": "hilbert16-kk-plus-one-core/v1",
  "translate_p": [
    2,
    0
  ],
  "what_this_is_not": [
    "not a dent of H(n)",
    "not two hyperbolic cycles",
    "not an explicit Hopf perturbation",
    "not H(4) >= 2 as a published improvement"
  ]
}